The contribution of Multi-GNSS Experiment (MGEX) to precise point positioning

This paper describes a process by which Global Navigation Satellite System (GNSS) nominal statistics and fault rates can be assessed with high confidence. The use of a GNSS in Advanced Receiver Autonomous Integrity Monitoring (ARAIM) requires knowledge of the level of performance of the signal-in-space (SIS) user range error (URE) in both nominal and faulty conditions. The performance characterization is done through a careful analysis of historical data, from which a determination of whether or not it meets the performance commitments of the constellation service provider (CSP) can be made. Typically, this analysis is carried out though a comparison of the broadcast navigation messages with post-processed precise estimates of the satellite clock and orbit states. This paper highlights the issues with such an approach as well as mitigation strategies to those issues. The issues primarily impact the estimates of fault rates rather than nominal statistics, as the number of faults is small compared to the overall amount of nominal data. In particular, methods of ensuring integrity in the logged broadcast navigation messages and precise clock and orbit products used in the analysis are described. In order to verify precise clock and orbit products, a Kalman filter (KF) to produce independent GNSS clock bias estimates has been developed and tested. The KF leverages the International GNSS Service (IGS) receiver network to produce estimates of GNSS clock biases given precisely known positions of the receivers as well as precise satellite orbit products. The KF serves multiple purposes in detecting and verifying faults. First, when only low rate (5 or 15 minute) clock products are available, higher rate products can be produced to detect short faults. Second, when precise clock products are available, the KF serves as a secondary check to protect against erroneous external precise products, which have been observed. Initial testing of the filter has shown an RMS error of under 20 centimeters for a five day run of GPS clock bias estimates, which is sufficient performance for precise product verification and fault detection.

Precise Point Positioning (PPP) is a popular technology for precise applications based on the Global Navigation Satellite System (GNSS). Multi-GNSS combined PPP has become a hot topic in recent years with the development of multiple GNSSs. Meanwhile, with the operation of the real-time service (RTS) of the International GNSS Service (IGS) agency that provides satellite orbit and clock corrections to broadcast ephemeris, it is possible to obtain the real-time precise products of satellite orbits and clocks and to conduct real-time PPP. In this contribution, the real-time multi-GNSS orbit and clock corrections of the CLK93 product are applied for real-time multi-GNSS PPP processing, and its orbit and clock qualities are investigated, first with a seven-day experiment by comparing them with the final multi-GNSS precise product ‘GBM’ from GFZ. Then, an experiment involving real-time PPP processing for three stations in the Multi-GNSS Experiment (MGEX) network with a testing period of two weeks is conducted in order to evaluate the convergence performance of real-time PPP in a simulated kinematic mode. The experimental result shows that real-time PPP can achieve a convergence performance of less than 15 min for an accuracy level of 20 cm. Finally, the real-time data streams from 12 globally distributed IGS/MGEX stations for one month are used to assess and validate the positioning accuracy of real-time multi-GNSS PPP. The results show that the simulated kinematic positioning accuracy achieved by real-time PPP on different stations is about 3.0 to 4.0 cm for the horizontal direction and 5.0 to 7.0 cm for the three-dimensional (3D) direction.

To obtain the coordinates by means of precise point positioning (PPP) technique we need to use the undifferenced GPS pseudocode and carrier phase observations but to obtain the “precise” positioning we need precise orbit and clock data too. This products and other information for obtaining the results by using PPP technique on a centimeter level accuracy can be downloaded from different locations, but the most reliable satellite ephemerides and clock correction are available from International GNSS Service (IGS). In the PPP analysis we determined the parameters such as the receiver clock error, ionospheric delays code biases, code multipath and the total neutral atmosphere delay of the observations. For the determination of the permanent station coordinates, using the PPP technique, we used precise orbit and clock solutions to enable absolute positioning of a single receiver. In this article we present the results obtained by using the PPP technique on the permanent station Oradea, from which we can conclude that the PPP technique can be used for different GNSS application.

Real-time precise orbit and clock products are crucial for real-time high-precision precise point positioning (PPP). The key for precise orbit prediction is to precisely determine the initial conditions (satellite position, velocity at the initial epoch) and the solar radiation pressure (SRP) parameters using an arc of known precise orbits. The optimal arc length will be investigated for precise orbit prediction, with which the high-accuracy satellite clocks can be estimated. The orbit prediction accuracies with different arc lengths and conditions over time are also investigated. The results indicate that the predicted orbit accuracy is governed by the SRP parameters. In addition, the predicted orbits and estimated clocks are evaluated quantitatively with respect to PPP solutions during in and out of eclipses seasons, based on which the optimal arc length is identified. The numerical results show that high-accuracy orbital prediction can be achieved using an arc length between 36 and 48 h and generally an arc length of 42 h is considered to be optimal. With this optimal arc length, the estimated clock accuracy is 0.048 and 0.122 ns for a prediction interval of 6 and 24 h, respectively. The average PPP ambiguity fix-rates with a prediction interval of 6 h are 80.2 and 84.7 % over an observation period of 30 min and 1 h, respectively.

This paper will address issues related to Precise Point Positioning (PPP) and perform raw observation data analysis to evaluate the specific performance of PPP based its all solutions processed by CSRS-PPP using final precise orbit and clock products from IGS. For this purpose, daily sessions of observations, at 30 seconds intervals, of five different IGS stations are processed using aforementioned approach. The tests show that, the solution accuracy reaches averagely 0.0023 m, -0.0005 m, -0.0035 m for static mode and about 5 cm for kinematic mode, respectively; centimeter convergence is obtained after being processed for 10-20 min, and residuals are nearly close to true-value after 30 min or more longer; tropospheric zenith delay estimates, both for static and kinematic, are greatly consistent with the solutions from IGS, and fluctuate within 5 mm; the residuals for clock offset are approximate to 0.1 ns about 1 h later, and the final values are close to 0 for three stations. It also may be inferred that carrier-phase ambiguity, real or integer, can play a pivotal role in aforementioned solutions.

The Fractional Cycle Bias (FCB) product is crucial for the Ambiguity Resolution (AR) in Precise Point Positioning (PPP). Different from the traditional method using the ionospheric-free ambiguity which is formed by the Wide Lane (WL) and Narrow Lane (NL) combinations, the uncombined PPP model is flexible and effective to generate the FCB products. This study presents the FCB estimation method based on the multi-Global Navigation Satellite System (GNSS) precise satellite orbit and clock corrections from the international GNSS Monitoring and Assessment System (iGMAS) observations using the uncombined PPP model. The dual-frequency raw ambiguities are combined by the integer coefficients (4,− 3) and (1,− 1) to directly estimate the FCBs. The details of FCB estimation are described with the Global Positioning System (GPS), BeiDou-2 Navigation Satellite System (BDS-2) and Galileo Navigation Satellite System (Galileo). For the estimated FCBs, the Root Mean Squares (RMSs) of the posterior residuals are smaller than 0.1 cycles, which indicates a high consistency for the float ambiguities. The stability of the WL FCBs series is better than 0.02 cycles for the three GNSS systems, while the STandard Deviation (STD) of the NL FCBs for BDS-2 is larger than 0.139 cycles. The combined FCBs have better stability than the raw series. With the multi-GNSS FCB products, the PPP AR for GPS/BDS-2/Galileo is demonstrated using the raw observations. For hourly static positioning results, the performance of the PPP AR with the three-system observations is improved by 42.6%, but only 13.1% for kinematic positioning results. The results indicate that precise and reliable positioning can be achieved with the PPP AR of GPS/BDS-2/Galileo, supported by multi-GNSS satellite orbit, clock, and FCB products based on iGMAS.

In recent years, many national timing laboratories (NMIs) have installed geodetic global positioning system (GPS) receivers together with their traditional GPS/GLONASS Common View (CV) receivers and two way satellite time and frequency transfer (TWSTFT) equipment. Many of these geodetic receivers operate continuously within the international GNSS service (IGS), and their data are regularly processed by IGS Analysis Centers. From its global network of over 350 stations and its Analysis Centers, the IGS generates precise combined GPS precise ephemeredes and station and satellite clock time series referred to the IGS Time Scale. A processing method called precise point positioning (PPP) is in use in the geodetic community allowing precise recovery of GPS antenna position, clock phase and tropospheric delays by taking advantage of the IGS precise products. Natural resources Canada (NRCan) has developed software implementing the PPP methodology. A previous assessment of PPP, as a promising time transfer method, was carried out at INRiM (formerly IEN) in 2003 [7], showing better stability over short/medium term than GPS CV and GPS P3 methods. Further analysis was carried out in 2005 [12] where, running continuously for period of up of two weeks, the NRCan PPP software was able to reduce the day-boundary discontinuities, allowing specific time-limited campaigns (PTFs). This paper reports on follow-on work performed at INRiM and NRCan to further characterize the PPP method for time transfer applications, involving some of the National Metrology Institutes considered in 2005. We take advantage of continuous PPP processing to develop a procedure to improve the continuity of solutions and to reduce the solution boundary discontinuities present in the daily PPP results.

Global Navigation Satellite System (GNSS) based Precise Point Positioning (PPP) has become the de facto standard for precise real-time offshore positioning applications. Current precision is of the order of 3−5 cm horizontally and twice this value for the vertical. However, this may not yet be good enough for tidal applications. In this contribution we will discuss new developments at Fugro, one of the world’s main providers of precise offshore real-time GNSS positioning services, to further improve PPP precision to the 2−3 cm level in the vertical component worldwide. For demanding applications, it is possible to even further improve this precision. These developments are based on merging PPP techniques (use of precise satellite orbits and clocks) with Integer Ambiguity Resolution (IAR), known from GNSS Real-Time Kinematic (RTK) positioning techniques. PPP IAR requires the generation and distribution to mobile users of Uncalibrated Phase Delays (UPDs) a network of reference stations. The network can be as small as one station or cover the entire globe. Once applied to the data of a mobile receiver, the carrier ambiguities should be integer. Fixing of these ambiguities to their proper integer value will result in significantly improved positioning performance. The infrastructure used to generate precise orbits, clocks and UPDs will be discussed. PPP IAR results will be shown from regional and global test beds, based on Fugro’s precise orbits and clocks for all currently available GNSSs. In addition, it will be shown that the introduction of new systems and signals, like triple-frequency GPS, Galileo and BeiDou, will help to significantly reduce the time required for PPP IAR solutions to converge to this centimeter level of accuracy.

Acousto-optic devices using lead molybdate and related compounds: Bell Telephone Labs Inc US patent 3617931 (1971) filed 5 May 1969

Ground-based GNSS ZTD/IWV estimation system for numerical weather prediction in challenging weather conditions

The BeiDou navigation satellite system (BDS) currently has 41 satellites in orbits and will reach its full constellation following the launch of the last BDS satellite in June 2020 to provide navigation, positioning, and timing (PNT) services for global users. In this contribution, we investigate the characteristics of inter-system bias (ISB) between BDS-2 and BDS-3 and verify whether an additional ISB parameter should be introduced for the BDS-2 and BDS-3 precise point positioning (PPP). The results reveal that because of different clock references applied for BDS-2 and BDS-3 in the International GNSS Service (IGS) precise satellites clock products and the inconsistent code hardware delays of BDS-2 and BDS-3 for some receiver types, an ISB parameter needs to be introduced for BDS-2 and BDS-3 PPP. Further, the results show that the ISB can be regarded as a constant within a day, the value of which is closely related to the receiver type. The ISB values of the stations with the same receiver type are similar to each other, but a great difference may be presented for different receiver types, up to several meters. In addition, the impact of ISB on PPP has also been studied, which demonstrates that the performance of kinematic PPP could be improved when ISB is introduced.

Assessment of L5 frequency on real-time GPS orbit and clock estimation

The International GNSS Service (IGS) Tide Gauge Benchmark Monitoring Working Group (TIGA-WG) is responsible for analyzing GNSS data from stations at or near tide gauges (TG) on a preferably continuous basis and to provide information specifically for the vertical rates. The position and vertical velocity results of the stations can be applied in several geodetic and geophysical applications, such as global and regional sea-level change, calibration of satellite altimeters and the unification of height systems. As one of the TIGA Analysis Centers the German Research Centre for Geosciences (GFZ) is contributing to the IGS TIGA Reprocessing Campaign (TIGA REPRO2). The solutions of the GFZ TIGA REPRO2 will also contribute to IGS second Data Reprocessing Campaign (IGS REPRO2) with the GFZ IGS REPRO2 solution. Following the first IGS reprocessing finished in 2010 some improvements were implemented into the latest GFZ software version EPOS.P8: reference frame IGb08 based on ITRF2008, antenna calibration igs08.atx, geopotential model (EGM2008), higher-order ionospheric effects, new a priori meteorological model (GPT2), VMF mapping function, and other minor improvements. GNSS data of the globally distributed tracking network of 794 stations for the time span from 1994 until end of 2012 are used for the GFZ TIGA REPRO2. To handle such large networks a new processing strategy is developed and described in detail. In the GFZ TIGA REPRO2 the GNSS@TG data are processed in precise point positioning (PPP) mode to clean data using the GFZ IGS REPRO2 orbit and clock products. To validate the quality of the PPP coordinate results the rates of 80 GNSS@TG station vertical movement are estimated from the PPP results using Maximum Likelihood Estimation (MLE) method. The rates are compared with the solution of University of La Rochelle Consortium (ULR) (named ULR5). 56 of the 80 stations have a difference of the vertical velocities below 1 mm/year. The error bars of PPP rates are significantly larger than those of ULR5, which indicates large time correlated noise in the PPP solutions.

For precise positioning in arctic regions with Global Navigation Satellite Systems (GNSS), such as GPS and Glonass, there are a number of issues to be resolved or taken into account. The most important ones are satellite geometry, ionospheric effects and distribution of correction data. Precise Point Positioning (PPP) is currently the standard for precise offshore positioning. PPP requires a sparse global network of GNSS reference stations to estimate precise satellite orbit and clock parameters in real-time. These parameters are transmitted to users, who can compute their position with an accuracy of 0.1 m using code and carrier observations. The main disadvantage of PPP is that in general it takes a long time to converge to this accuracy, about 30–45 minutes. GNSS carrier observations are similar to pseudo ranges, but have an additional bias which needs to be estimated. Under certain conditions, these biases are integer. This property is used in what is generally referred to as Real-Time Kinematic (RTK) positioning, a technique which uses corrections generated at reference stations to make sure these ambiguities are integer. Integer Ambiguity Resolution (IAR) results in RTK accuracies of 0.01–0.03 m or better and short convergence times, ranging from instantaneous to several minutes for long inter-station distances. The disadvantage is the limited area of applicability, because RTK in general does not use precise orbits and clocks. Current research focuses on the combination of PPP and RTK techniques. The main goal is to achieve cm accuracy with a sparse network of reference stations. Another goal is to reduce convergence time. Applications are in the field of precise real-time offshore positioning in general, and subsidence monitoring and tidal estimation in particular. Results will be presented from standard PPP and PPP combined with IAR for arctic regions and from a test bed in the Gulf of Mexico. These results, although preliminary, indicate centimeter level accuracy is indeed possible, also in the arctic. We will also look at further improvements, mainly in convergence time, using all operational satellites and signals from current and future navigation systems.

Precise point positioning (PPP) is highly dependent on the precise ephemerides and satellite clock products that are used. Different ephemeris and clock products are available from a variety of different organizations. The aim of this paper is to assess the achievable static positioning accuracy and precision when using different precise ephemerides from three analysis centres Natural Resources Canada (EMX), European Space Agency (ESA) and GeoForschungsZentrum (GFZ), using GPS alone, GLONASS alone, and GPS and GLONASS combined. It will be shown in this paper that the precise products are significantly affected by the time-base of the reference stations, and that this is propagated through to all the estimated satellite clocks. In order to overcome the combined biases in the estimated satellite clock, in the PPP processing, these clocks errors need to be handled with an appropriate variation in the estimated receiver clock. It will also be shown that the precise coordinates of the satellites differ between the analysis centres, and this affects the PPP position estimation at the millimetre level. However, all those products will be shown to result in the same level of precision for all coordinate components and are equivalent to the horizontal precision from a Global Double Difference (GDD) solution. For the horizontal coordinate component, the level of agreement between the PPP solutions, and with the GDD solution, is at the millimetre level. There is a notable, but small, bias in the north coordinate components of the PPP solutions, from the corresponding north component of the GDD solutions. It is shown that this difference is due to the different strategy adopted for the GDD and PPP solutions, with PPP being more affected by the changing satellite systems. The precision of the heights of the receiver sites will be shown to be almost the same across all the PPP scenarios, with all three products. Finally, it will be concluded that accuracy of the height component is system dependent and is related to the behaviour of antenna phase centre with the different constellation type.